This interaction is notably affected by a scattering of the electrons around the initial trajectory (forward scattering effect) as well as by a backscattering (backward scattering effect). These effects, referred to as proximity effects, depend notably on the materials of the target and its geometry. Whatever the reason for desiring to perform this electron bombardment (etching, imaging or analysis), it is therefore necessary to take account of the proximity effects in order to obtain a result which is faithful to the objective sought. A correction of the proximity effects is therefore performed. Accordingly, it is known to predict them through a model so as to take account thereof in the calculation of the electron radiation doses used to bombard the target. It is accordingly known to use a so-called point spread or scattering function (or PSF) and the PSF is convolved with the geometry of the target. A commonly used PSF is a combination of Gaussians, a first Gaussian to model forward scattering (PSF of the forward scattering), and one or more additional Gaussians to model the backscattering (PSF of the backscattering).
The equation of the PSF is thus traditionally represented by a function f(x,y) of the following form:
      f    ⁡          (      ξ      )        =            1              π        ⁡                  (                      1            +            η                    )                      ⁢          (                                    1                          α              2                                ⁢                      e                                          -                                  ξ                  2                                                            α                2                                                    +                              η                          β              2                                ⁢                      e                                          -                                  ξ                  2                                                            β                2                                                        )      With the following notation:                α is the width of the direct radiation;        β is the backscattering width;        η is the ratio of the intensities of the direct and backscattered radiations.        ξ is the radial position of a pointThe values of the parameters α, β and η can be determined experimentally for a given method. These parameters are dependent on the acceleration voltage of the machine and the target. Typically for an acceleration voltage of the order of 50 KV and a silicon or glass target (SiO2), α is of the order of 30 nm, β of the order of 10 μm and η of the order of 0.5.        
However, if the energy distribution around the impact point, given by a PSF of this double Gaussian type, is compared with that produced by a simulation using a Monte-Carlo model, significant deviations are noted. The simulations of Monte-Carlo type, referred to in the subsequent description as the reference model, are closer to the experimental results but are difficult to use in production because of the long calculation times necessary for the simulation. An indicator of the quality of a model will therefore be the “fit” between the PSF used and the reference model, the fit being measured by the sum of the quadratic deviations between the two curves representing the two models on a normalized sample size of points.
It appears particularly useful to find forms of a PSF that are closer to the simulation results and experimental results but that can be parametrized and therefore calculated in a much shorter time than Monte-Carlo simulations.